Does variable step size ruin a symplectic integrator?
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The development of variable-step symplectic integrators with application to the two-body problem
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Comparison of splitting algorithms for the rigid body
Journal of Computational Physics
On the Preservation of Invariants by Explicit Runge--Kutta Methods
SIAM Journal on Scientific Computing
Short Note: Reducing round-off errors in rigid body dynamics
Journal of Computational Physics
Initializers for RK-Gauss methods based on pseudo-symplecticity
Journal of Computational and Applied Mathematics
Energy-preserving methods for Poisson systems
Journal of Computational and Applied Mathematics
Line integral methods which preserve all invariants of conservative problems
Journal of Computational and Applied Mathematics
Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems
Numerical Algorithms
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This paper is concerned with the long term behaviour of the error generated by one step methods in the numerical integration of periodic flows. Assuming numerical methods where the global error possesses an asymptotic expansion and a periodic flow with the period depending smoothly on the starting point, some conditions that ensure an asymptotically linear growth of the error with the number of periods are given. A study of the error growth of first integrals is also carried out. The error behaviour of Runge-Kutta methods implemented with fixed or variable step size with a smooth step size function, with a projection technique on the invariants of the problem is considered.